An adaptive moving total least squares method for curve fitting

• An Adaptive Moving Total Least Squares (AMTLS) method is presented.
• The direction of local approximants is considered in AMTLS method.
• AMTLS method integrates MLS method and MTLS method.
• Experiments confirm the validity of AMTLS method.

The moving least squares (MLS) method and the moving total least squares (MTLS) method have been developed to deal with the measured data contaminated with random error. The local approximants of MLS method only take into account the error of dependent variable, whereas MTLS method considers the errors of all the variables, which determines the local approximants in the sense of the total least squares. MTLS method is more reasonable than MLS method for dealing with errors-in-variables (EIV) model. But because of the weight function with compact support, it is complicated to choose fitting method for the best performance. This paper presents an Adaptive Moving Total Least Squares (AMTLS) method for EIV model. In AMTLS method, a parameter λ associated with the direction of local approximants is introduced. MLS method and MTLS method can be considered as special cases of AMTLS method. Curve fitting examples are given to prove the better performance of AMTLS method than MLS method and MTLS method.